The American, who is seeded sixth next week, outgunned Baghdatis in 76 minutes to emulate the achievement of his compatriot Michael Chang, who won the exhibition event from 1995 to 1997.
"Is there a three-for-one special where you can swap three titles here for one Australian Open?" Roddick joked in an on-court presentation.
"It's been a great week. I hope the form I showed this week will be indicative of how I play next week."
Both players were solid on serve early on, but Baghdatis had a break point to lead 5-4 only for Roddick to dig himself out of trouble with a strong second serve.
The first set looked to be heading for a tiebreak only for the Cypriot to slip up in the 12th game, handing Roddick the set.
An early break in the second set put Roddick in control and once he had saved three break points in the seventh game, he eased to victory, sealing the win with his 10th ace.
Baghdatis, who was a last-minute replacement for world number one Roger Federer, who had a stomach virus, said his form was not quite what it was when he reached the final of the Australian Open in 2006.
"I need some matches," he said.
"I think the most important thing for me is to get through the first two rounds. If I do, then I will feel confident that I can go further."
Roddick begins against a qualifier at Melbourne Park, while Baghdatis plays former Australian Open champion Thomas Johansson of Sweden.
Tursunov takes title
Dmitry Tursunov beat upstart Australian left-hander Chris Guccione 7-6 (3), 7-6 (4) on Saturday to win the Sydney International men’s singles title, reports AP
Tursunov, a California-based Russian, withstood a furious serving onslaught from Guccione, who only lost 10 points on his serve and had 15 aces.
It was the first ATP tour final for Guccione, who had beaten compatriot and No. 6 seed Lleyton Hewitt and No. 4 seed.
Kohlschreiber wins
German seventh seed Philipp Kohlschreiber upset former world number one Juan Carlos Ferrero 7-6, 7-5 to claim the Auckland Open title, adds Reuters from Wellington.
Kohlschreiber blasted seven aces but undid his good work with seven double faults, including two in the final game of the match, before winning his second ATP Tour title.
"I was telling myself to relax, stay cool," Kohlschreiber told reporters of the final game. "The next point was very important and once I won that I knew I had a chance to seal the match."
Kohlschreiber, a quarterfinalist at Doha last week, said he was hoping his recent form would propel him into the world top-20 this year. "That is one of my goals. I'd like to get there as soon as possible."
Ferrero has not won an ATP tour title since the Madrid Masters in October 2003 and has now played six successive finals without a win.